Final answer:
To solve the system of linear inequalities, graph both lines on the same coordinate plane and look for the overlapping region that satisfies both conditions. The solution is the area above y = 5x + 7 and below y = 3x + 12, up to the intersection point of these lines.
Step-by-step explanation:
To find the solution of the system of linear inequalities y < 3x + 12 and y ≥ 5x + 7, we need to consider the region of the coordinate plane that satisfies both conditions simultaneously. The inequality y < 3x + 12 means that the solution area is below the line y = 3x + 12. The inequality y ≥ 5x + 7 indicates that the solution area is above or on the line y = 5x + 7.
By graphing both inequalities on the same coordinate plane, we can visually identify the solution area. The overlapping region, if it exists, will be the set of points that satisfy both inequalities. However, since the slope of the second line (5) is steeper than the slope of the first line (3), the lines will eventually intersect. The solution will therefore be the region that lies above the second line and below the first line, ending at their point of intersection.